<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In this study, we introduce the relationship between the Tutte polynomials and dichromatic polynomials of (2,n)-torus knots. For this aim, firstly we obtain the signed graph of a (2,n)-torus knot, marked with {+} signs, via the regular diagram of its. Whereupon, we compute the Tutte polynomial for this graph and find a generalization through these calculations. Finally we obtain dichromatic polynomial lying under the unmarked states of the signed graph of the (2,n)-torus knots by the generalization.</p>
</abstract>

In this study, we introduce the relationship between the Tutte polynomials and dichromatic polynomials of (2,n)-torus knots. For this aim, firstly we obtain the signed graph of a (2,n)-torus knot, marked with {+} signs, via the regular diagram of its. Whereupon, we compute the Tutte polynomial for this graph and find a generalization through these calculations. Finally we obtain dichromatic polynomial lying under the unmarked states of the signed graph of the (2,n)-torus knots by the generalization.

Dichromatic polynomial for graph of a (2,n)-torus knot

Department of Mathematics, Faculty of Science and Letters

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

{"article-title":"Dichromatic polynomial for graph of a (2,n)-torus knot"}

In this study, we introduce the relationship between the Tutte polynomials and dichromatic polynomials of (2,n)-torus knots. For this aim, firstly we obtain...

Dichromatic polynomial for graph of a (2,n)-torus knot

Published Online: Dec 31, 2020

Page range: 397 - 402

Received: Jun 24, 2019

Accepted: Oct 10, 2019

DOI: https://doi.org/10.2478/amns.2020.2.00068

Keywords
Knot, knot graph, Tutte polynomial, dichromatic polynomial, signed graph

© 2020 Abdulgani Şahin, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

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Dichromatic polynomial for graph of a (2,n)-torus knot

Published Online: Dec 31, 2020

Page range: 397 - 402

Received: Jun 24, 2019

Accepted: Oct 10, 2019

DOI: https://doi.org/10.2478/amns.2020.2.00068

KeywordsKnot, knot graph, Tutte polynomial, dichromatic polynomial, signed graph

© 2020 Abdulgani Şahin, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Keywords
Knot, knot graph, Tutte polynomial, dichromatic polynomial, signed graph